Visualization of deep blood vessels using principal

component analysis based laser speckle imaging.JOSE ANGEL ARIAS-CRUZ,1 ROGER CHIU,2.* HAYDE PEREGRINA-BARRETO,1 RUBEN RAMOS-GARCIA,1 TERESITA SPEZZIA-MAZZOCCO,1,3 AND JULIO C RAMIREZ-SAN-JUAN1

1Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro 1, Tonantzintla, Puebla, México2Departamento de Ciencias Exactas y Tecnología, Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Díaz de León 1144, Paseos de la Montaña Lagos de Moreno

Jalisco, México3Catedras CONACYT, Cd. De México, México

*angelarias01@gmail.com

Visualization of blood vessels is a fundamental task to evaluate the health and

biological integrity of the tissue. Laser Speckle Contrasts Imaging (LSCI) is a non-

invasive technique to determine the blood flow in superficial or exposed vasculature.

However, the high scattering of biological tissue, hinder the visualization of those

structures. In this paper, we propose the use of Principal Component Analysis (PCA) in

combination with LSCI to improve the visualization of deep blood vessel. Using PCA,

it be separated and filtrated by selecting the most significant principal components.

This analysis was applied to in vitro samples, and our results demonstrate that this

approach allows the visualization and localization of blood vessels as deep as 1000 µm.

Introduction

Materials and method

Fig.2 a) LSI system , b) top-layer thicknesses[5] (TLTs) of δ = 0,190, 510, 311 and 1000 μm. We used a syringe pump to infuse intralipid at 3% in water as a blood substitute into the channel at

speed of 5 mm/s, glass capillary tube, with an inner diameter of 550 μm and Region of interest(ROI) centered .

The local contrast K [1]. is computed typically in a sliding window of 5x5 pixels

through the equation

𝐾 =σ

<𝐼>(1)

where σ is the standard deviation and < 𝐼 > is the mean intensity of the pixels in the

sliding window, this local contrast value is assigned to the central pixel.

The contrast equation (1) can be expressed [2] as a function of the correlation time τcof the backscattered light from the sample and the exposure time T of the CCD

camera[3]:

𝐾2 𝑥

= 𝛽𝜌2exp −2𝑥 − 1 + 2𝑥

2𝑥2+ 4𝛽𝜌 1 − 𝜌

exp −𝑥 − 1 + 𝑥

𝑥2+ 𝛽 1 − 𝜌 2 (2)

where 𝑥 ≡ 𝑇/𝜏𝑐 , ρ is the fraction of the dynamically scattered light and β is a

correction factor that depends on the ratio of speckle and pixel size. When 𝑥 ≫ 1, the

contrast reaches an asymptotic value (KS) given by:

𝐾2 𝑥 |𝑥≫1 ≡ 𝐾𝑠2 = 𝛽 1 − 𝜌 2 3

Separate out 𝐾𝑆2 from 𝐾𝐷

2 and therefore improve the visualization of deep blood

vessels.

Laser speckle imaging

PCA is a statistical technique that uses an orthogonal transformation to describe a set

of correlated observations in terms of new uncorrelated variables, called principal

components (PC’s), which are linear combinations of the original variables [4]. The

procedure to obtain the PC’s begins with the organization of the data in a matrix Γ of

dimension M x N. Here M represents the number of observations and N the number

of variables

PCA

Fig. 1 a) organization of images in a new data matrix a) a set of 30 raw speckle images are

arrangement into matrix Γ, given by Eq. 4. N corresponds to number of image (N = 1 to 30) and

M corresponds to image pixel (M =1 to 640x480), b) original space , and PC’s space.

Results and discussion

Fig. 3 A) Eigenvalue vs the number of PC, the thick red horizontal line establishes the separation

by means of the Guttan-Kaiser B) . Contrast images for groups C;A and C-A. C) Experimental 𝐾2 (symbols) as function of T for different δ and its theoretical adjustmen.

Comparison between the traditional LSCI (C) and our proposal C-A with their corresponding

segmentation by K-means (2nd and 4th columns).

Fig. 5. a) Location of the capillary [6] (vertical lines) of the profiles for C, b) similarly for C-A, c) Actual and estimated capillary (vessel) width for different δ values

ConclusionsIn this work, we demonstrate that PCA applied to LSCI allow us to separate out the

static component from the dynamic component in the raw speckle images achieving

visualization of blood vessels as deep as 1000 μm. In addition, employing kurtosis on

the dynamic region (such as flow in the capillary) we demonstrated a more accurate

estimation of the actual vessel width. It is important to mention that our proposal

works well when the variance between the raw speckle images is enough to be

distributed among all the PCA, for example when the dynamic of the sample is

relatively low or for short exposure times. Otherwise the first component attracts most

of the information compared with the rest of the component and the filtering process

fails.

References1. A. Fercher and J. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt Commun, vol. 37, pp. 326–329, 1981.

2. B. Parthasarathy, J. Tom, A. Gopal, X. Zhang, and K. Dunn, “Robust flow measurement with multi-exposure speckle imaging”, Opt. Express 16, 1975

(2008).

3. Ramirez-San-Juan JC, Ramos-Garcia R, Martinez-Niconoff G and Choi B; Simple correction factor for laser speckle imaging of flow dynamics; Optics

Letters 39(3), 678-681, (2014).

4. H. Abdi, and L. J. Williams, “Principal component analysis,” Wiley Interdiscip. Rev.: Comput. Statistics 2, 433–459 (2010).

5. F. Ayers, A. Grant, D. Kuo, D. J. Cuccia, and A. J. Durkin, “Fabrication and characterization of silicone-based tissue phantoms with tunable optical

properties in the visible and near infrared domain,” in Proc. SPIE, 2008), 6870E.

6. H. Peregrina-Barreto, E. Perez-Corona, J. Rangel-Magdaleno, R. Ramos-Garcia, R. Chiu, and J. C. Ramirez-San-Juan, "Use of kurtosis for locating deep

blood vessels in raw speckle imaging using a homogeneity representation," J. Biomed. Opt. 22, 066004 (2017).

a) b)

Frame 1

Frame 2

Frame 29

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PC29

a) b)

X Congreso Nacional de Tecnología Aplicada a Ciencias de la Salud

0.1 1 100.00

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PC 1:1 PC 2:30 PC 1:30A B C

550 μm

C A C-A

𝜆 =

𝜆𝑗𝑁

𝑗=1

𝑁

A)

B)

C)

δ=0 µm

δ=190 µm

δ=311 µm

δ=510 µm

δ=1000 µm

C Seg(C) C-A Seg(C-A)

550 μm

a) b)

Δ

(µm)

Actual width

(pixel)

Seg(C)

(pixel)

Error

(%)

Seg(C-A)

(pixel)

Error

(%)

0 70 84 20 70 0510 70 94 37 78 11

1000 70 170 143 90 28

c)